Simple fraction , can someone help = 3 4 − 2 k + 3 2 ( k + 1 ) ( k + 2 ) + 1 ( k + 1 ) ( k + 3 ) how can i simplify above fraction please, can someone guide me from beginning to the end?help am a beginneri took the LCM of both to be 4(k+1)(k+2)(k+3)4 into the LCM =(k+1)(k+2)(k+3) 2(k+1)(k+2) in to the LCM =2(k+3) (k+1)(k+3) in to the LCM = 4(k+2)therefore = ( k + 1 ) ( k + 2 ) ( k + 3 ) − 2 ( k + 3 ) ( 2 k + 3 ) + 4 ( k + 2 ) 4 ( k + 1 ) ( k + 2 ) ( k + 3 )

Question

Simple fraction , can someone help  =      3    4    −            2      k      +      3              2      (      k      +      1      )      (      k      +      2      )        +      1          (      k      +      1      )      (      k      +      3      )      how can i simplify above fraction please, can someone guide me from beginning to the end?help am a beginneri took the LCM of both to be 4(k+1)(k+2)(k+3)4 into the LCM =(k+1)(k+2)(k+3) 2(k+1)(k+2) in to the LCM =2(k+3) (k+1)(k+3) in to the LCM = 4(k+2)therefore   =            (      k      +      1      )      (      k      +      2      )      (      k      +      3      )      −      2      (      k      +      3      )      (      2      k      +      3      )      +      4      (      k      +      2      )              4      (      k      +      1      )      (      k      +      2      )      (      k      +      3      )

dheasca8d · Accepted Answer

First you want to put everything over a common denominator, which should be a multiple of all the denominators. Here you would go for   4  (  k  +  1  )  (  k  +  2  )  (  k  +  3  )Now you need to multiply top and bottom of each fraction in turn by the appropriate amount to make the bottom what you are aiming for. So you get            3      (      k      +      1      )      (      k      +      2      )      (      k      +      3      )              4      (      k      +      1      )      (      k      +      2      )      (      k      +      3      )        −            (      2      k      +      3      )      2      (      k      +      3      )              2      (      k      +      1      )      (      k      +      2      )      2      (      k      +      3      )        +            4      (      k      +      2      )              (      k      +      1      )      (      k      +      3      )      4      (      k      +      2      )      which equals            3      (      k      +      1      )      (      k      +      2      )      (      k      +      3      )      −      2      (      2      k      +      3      )      (      k      +      3      )      +      4      (      k      +      2      )              4      (      k      +      1      )      (      k      +      2      )      (      k      +      3      )        .Next you need to expand out each product in the top, and collect like terms. When you&#039;ve done that you should try to factorise the top and cancel any common factor with the bottom. If you&#039;ve done it right, you should get a common factor of   (  k  +  1  )

=3/4-(2k+3)/(2(k+1)(k+2))+(1)/((k+1)(k+3)) how can i simplify above fraction please, can someone guide me from beginning to the end?

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